## APPENDIX 5: The Size of the Quantum Change

Puthoff’s analysis revealed that Pa (the power available for absorption from the random background ZPF by a charged harmonic oscillator) is given by

Pa = e23/ (24π2εm0c3)                               (116)

This is the power available from all directions of ZPF propagation, but only one third of the total energy of the field will be absorbed by the oscillator . Utilizable power, Pu , is then

Pu =  e23/ (72π2εm0c3)                                 (117)

Here, m0 is the “bare” mass of the point particle oscillator of resonance frequency ω. The changes at the jump considered here are due to the change in the utilizable energy or power available from the ZPE. If Eu is the utilizable energy available for absorption from the ZPE, then Eu is proportional to Pu. So, looking back in time, if the power maintaining the electron in its orbit before the jump is P1 and the power utilized after the jump is P2, then (23) gives us

U2/U1 = E2/E1 = 1(1+z) = P2/P1                     (118)

As a consequence, (118) can be written as

P1 = P2 + zP2                                                    (119)

Equation (119) indicates the increase in P2at the jump is given by the dimensionless fraction z. This requires z to be a dimensionless component of (117), that is 1/(72π2). But that does not exhaust the dimensionless components of P, since the electronic charge e is expressed in units of Coulombs, and one Coulomb is an Ampere-second. Now, by definition, the Ampere is proportional to a force per unit length, which has the same dimensions as energy per unit area. If the electron’s surface area is represented by a, and if we allow d to contain proportionalities, then

e = Coulombs = (energy/area) x time = (power/area) x time2 = d/a   (120)

In this equation, the electron surface area a can be replaced by a = 4πr02, where r0 is the “bare” electron radius. The dimensionless component of e that emerges from this is given by

e = d/a = D/(4π)                                                 (121)

where D also contains proportionality factors.  If the results of (121) are substituted in (117), then the utilizable power becomes

Pu = {[D/(4π)]23}/ (72π2εm0c3)                            (122)

From (122), the full dimensionless component making up the value of the redshift quantum nΔz when n=1 can finally be written as

{[1/(4π)]2}[1/(72π2)] = 1/(1152π4) = 1/112215 = 8.91144 x 10-6 = Δz         (123)

If we multiply Δz by c as in equation (28), the result in km/s can be compared with Tifft’s.

cΔz =(299792) x (8.91144 x 10-6) = 2.671 km/s                  (124)

This is close to Tifft’s 8/3 = 2.667 km/s and accounts for the observed quantum change.

References

 A.P. French, op. cit., p.82. (see Ref. #73)

Go to: first page, section 1, 2, 3, 4, 5, 6, 7 or appendix 1, 2, 3, 4, 5, 6, 7, 8, or tables, or figures 1-7, or figure 8 or reference page.